When you arrive at NRT and have your luggage and some cash, go to the JR Service Center (glass walls with green trim) and have all of your Rail Passes validated. Each person will have to validate his/her Pass. Once the Passes have been issued, have the same agent reserve your seats for both the Narita Express to Shinagawa and the Hikari to Kyoto and issue your seat tickets right then. If the line is too long, you can also do the exchange downstairs at the JR ticket window in the basement. Once you have your seat tickets, go down to the rail station in the basement, show your passes and seating tickets at the manned gate, go to the tracks and get on the train. The attendant at the gate can direct you to the right platform. Train number, platform number, car number and seat number will all be on the tickets. There are two rail companies in the basement. Make sure you go to the JR gates, not the Keisei.
Once at Shinagawa, follow the signs to the correct platform for your train to Kyoto and repeat. When the conductor passes through show him your Rail Passes. If there is time, I like to get a drink and small bento lunch box at a kiosk on the platform to eat on the train. Drink vending machines are also on the platform.
At Kyoto, I would use a cab to the hotel. There may be a hotel shuttle but I'm not sure. Someone else may know.
I have found the Kyoto prepaid bus pass to be helpful but I haven't travelled with such a crowd. You may find cabs to be almost as cheap when you pack people in. You will most likely need 2 cabs for 7 people although the hotel may be able to arrange a minivan-cab. You should probably look through some guides and have a list of destinations. 2 days is not enough to see everything so have a list. Another option would be a day tour with Mr. Doi in his minivan. He is very highly regarded.
http://www3.ocn.ne.jp/~doitaxi/
In Tokyo, you can get a prepaid Suica card or PASMO card at subway stations. Since your Rail Pass will cover any JR train travel in Tokyo, the PASMO might make the most sense for subways but the Suica (which would also cover JR train lines) will work as well.
http://www.pasmo.co.jp/en/
http://www.jreast.co.jp/e/pass/suica.html
I would just take a cab to the hotel from Tokyo Station. Others may disagree. I would NOT like to juggle luggage and 2 toddlers on the subway!
If you are certain of your desired train back to Tokyo, you can reserve seats immediately upon arriving at Kyoto. That way you can be more sure of getting all your seats together. I would probably wait until the day before and just stop by the station at my convenience. Others might say just get your seats as you are leaving but I prefer the certainty of advance reservations.